Algebra Help (question in description)

Question

In a round-robin chess tournament, each player is paired with every other player once. The function, shown below, models the number of chess games, N, that must be played in a round-robin tournament with t chess players. In a round-robin chess tournament, 36 games were played. How many players entered the tournament?

N = t^2-t over 2

How many players entered the tournament?

Answer 1

36=(t^2-t)/2

72=t^2-t

t^2-t-72=0

factor

(t-9)(t+8)=0

t-9=0

t=9 players

check:

player 1 plays 8 other people

player 2 plays 7 other people (players 1 and 2 already played each other)

player 3 plays 6

player 4 plays 5

player 5 plays 4

player 6 plays 3

player 7 plays 2

player 8 plays 1

player 9 already played with all the other players so player 9 doesn't have to play any more games

1+2+3+4+5+6+7+8=36